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1、扬州大学2014级高等数学Ⅰ(2)期中考试试题班级 学号 姓名 得分 一、选择题(每小题3分,共18分)1.对于二元函数,下列结论中正确的是( ).A.若偏导数与都存在,则必在点处连续B.若偏导数与都存在,则必在点处可微C.若与都存在,则必有D.若在点处可微,则在点处沿任一方向的方向导数都存在2.设函数的全微分为,则( ).A.不是极值,是极大值 B.不是极值,是极小值C.是极小值,是极大值 D.是极大值,是极小值3.设函数由方程确定,其中为可导函数,为常数,则( ). A. B. C. D.4.二次积分交换积分
2、次序后得( ).A. B.C. D.5.二次积分的极坐标形式为( ).otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,andDirectorofthenewOfficeinJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasb
3、eentheNorthwestOfficeoftheFederationofStateenterprisesMinister,ShenmufuguSARmissions,DirectorofNingxiaCountypartyCommitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand第5页 共6页A. B.C. D.6.设函数满足,则与依次为( ).A. B. C. D.二、计算题(每小题7分,共70分)7.设,求,及.8.设是由方程所确定的函数,求.ot
4、herstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,andDirectorofthenewOfficeinJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasbeentheNorthwestOfficeoftheFederationofStateenterp
5、risesMinister,ShenmufuguSARmissions,DirectorofNingxiaCountypartyCommitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand第5页 共6页9.设,其中函数具有二阶连续偏导数,求.10.求曲线在点处的切线方程与法平面方程.11.设函数,求(1)在点处沿从该到点的方向的方向导数;(2)在点处的方向导数的最大值.otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,an
6、dDirectorofthenewOfficeinJingdezhen,JiangxiCommitteeSecretary.Startingin1939servedasrecorderoftheWestNorthOrganization,SecretaryoftheSpecialCommitteeAfterthevictoryofthelongMarch,hehasbeentheNorthwestOfficeoftheFederationofStateenterprisesMinister,ShenmufuguSARmissions,DirectorofNingxiaCountypartyCo
7、mmitteeSecretaryandrecorderoftheCountypartyCommitteeSecretary,Ministersand第5页 共6页12.求二元函数的极值.13.在曲面的第一卦限部分上求一点,使这点到坐标原点的距离最短.otherstaffoftheCentre.Duringthewar,ZhuwastransferredbacktoJiangxi,andDirect